Lot 60 at the Savills property auction, held on Monday at the Marriott hotel in central London, inevitably attracted huge interest since it was advertised in advance as the most expensive council home ever to be sold, with a reserve price of £2.3m. The catalogue described the Southwark property as "an attractive pair of Grade II listed semi-detached buildings" in a "vibrant location close to Borough market, London Bridge, the Shard, the City and South Bank", adding, crucially: "Vacant."

By the time the building was sold, it was no longer vacant. Shortly before bidding began, a young woman stood up and told the room she had an announcement to make. "Excuse me. Sorry to interrupt," she began. "We are here to tell you that Lot No 60 is a council house that is currently being occupied by community activists who don't want to see this property lost, because we believe that council housing is a public good and it shouldn't be being sold. If you want to buy it, you're buying it with 20 squatters."

The announcement did nothing to dampen the enthusiasm for the sale, and the buildings sold for £2.96m.

At a time when a new frenzy is developing around London property, with average house prices in the capital rising by 9.3% year-on-year, the news of a £3m council house sale was headline news. The activists from Housing Action Southwark and Lambeth were aware of the potent symbolism of the sale, and seized the moment to highlight their concerns about the shrinking of London's council house stock.

Inside Britain's most expensive council house, a polite and organised protest is under way. Volunteers have drawn up a rota to ensure that the house is permanently occupied, and that there is a nightly team of volunteers to sleep in the drafty section of the house that they have taken over. One of the activists has contacted an electricity company to get a new account set up in his name, so that protesters cannot be charged with stealing electricity.

The protesters are not squatting in a traditional way, since none of them plans to live here permanently, and noone has moved anything in other than sleeping bags, blankets and an electric radiator. Someone has brought a Scrabble set to help while away the time; someone else has been practising a violin, balancing their sheet music on the mantelpiece.

From a bathroom window, with views on to the Shard, Borough market and the curved brick railway arches, activists have suspended sheets painted with the slogans: "Stop social cleansing!" and "Homes for all!" Inside they are at pains to cause no damage to the building, and have carefully removed the heavy steel anti-squatting door from its hinges and leaned it against the hallway wall.

A view of the Shard from the occupied Park Street property. Photograph: Sarah Lee for the Guardian Sarah Lee/Guardian

This is what you get for £3m in an area of central London that has been dramatically transformed since the opening of Tate Modern in 2000: two five-storey 1820 houses, built as homes for the managers of Anchor Brewery, one so structurally unsound that a complex mesh of scaffolding is propping it up. In the other, there are cracks big enough to stick a pencil into creeping up the stairway. The house has never been much modernised, so even with the light restricted by the metal grills bolted to the windows, you can see the period features that developers like, wooden shutters and fireplaces. The house is habitable, only recently vacated by a family with several children. Traces of their lives remain, a few stickers and scribbles on the children's bedroom walls. The nearest shop, about 30 metres along the road, is a Paul Smith boutique, selling pink woollen children's gloves for £45.

Given that Southwark has made a commitment to build 20 new council houses with the money generated by the sale of the property, this is not a clear-cut issue. Inside the house, sitting on the carpet in a chilly, second-floor bedroom, the protesters set out why they believe the sale was wrong.

Cathy Henderson, 38, a dance teacher and an adviser on housing issues explains that the protest is about more than simply the sale of 21 and 22 Park Street. She says the sale of a council house in such a central location, so close to the river and the tube, "has the effect of changing the character of this area; it is social cleansing, it is saying the only people who deserve to live in Zone 1 are people who aren't in social housing".

"For most of us, the issue isn't really the fate of this house, but the promises that Southwark council keeps making and breaking. We're not against the idea that Southwark could sell something and do something with the money that is more accessible and more the sort of houses that are needed. The issue that we have is that we don't trust them to do what they say they will do, because they have broken promises before."

She points to the nearby Heygate estate, in Elephant and Castle, which is being prepared for demolition. Heygate used to have 1,100 homes and will be replaced by a development that contains only 79 council properties amid a total of 2,535 homes. "It's not built to be council housing, it's not even built to be social housing; a lot of it is being built to be privately owned. A lot is being advertised and sold off-list before it's even finished, to investors, who see London as a really solid, stable place to invest their money. They could buy properties in London and keep them empty and still be guaranteed a profit three years later," she says.

Southwark council has mounted a staunch defence of its decision to sell. While it concedes there will be a lower than promised proportion of affordable housing in the redevelopment of the Elephant and Castle area (25% instead of 35%), it says that overall there will be "at least 1,650 affordable – including social rent and shared ownership – significantly more than were lost on the Heygate". Officials say 20 new homes are already being built in the same part of Southwark as Park Street.

Anna Minton, author of Ground Control, a study of flawed urban planning, who researched the Heygate development, was sceptical about the proportion of the new properties that would be genuinely affordable.

"The sell-off of an eye-catching £3m property is all of a piece with what they are doing across the borough: divesting themselves of social housing and replacing it with so-called affordable housing that isn't even affordable for people on average incomes, let alone people in social housing," she said.

Most of the protesters are in their 20s, and are not themselves council tenants; several are graduates, working, but struggling to afford to live in London. Ellie (who asked for her real name not to be printed), 25, who grew up in Brixton, is training to be an English for Speakers of Other Languages (ESOL) teacher, and is about to move back home to live with her mother because she cannot afford London rents. A volunteer with Housing Action Southwark and Lambeth, supporting local residents in their dealings with Southwark housing department, she has joined the protest because she sees the sale as emblematic of the speed with which central London is being transformed.

"It is about the rights of people on low incomes to live in this area. Council housing is a public good that everyone can benefit from. I don't want this house to be lost at a time when there is a massive need," she says. She is unconvinced by "Southwark's distant promises of building future council housing". "This building is here, right now, with maybe a lick of paint and some work to deal with cracks and the stairs, it could be livable in. We need council housing right now," she says.

She was the person who stood up in the Marriott to announce the occupation, and was surprised that there were murmurings of support in a hall filled with investors and developers.

"I thought it would be a sea of hate, but someone next to me said, 'You're absolutely right.' I wasn't booed and heckled. I was marched out. People either said nothing or were supportive. We were so surprised," she says.

"Council housing represented truly affordable, quality housing, and most people in London are struggling with high rents. There's a massive homelessness crisis. These things really resonate."

The issue of the unaffordability of central London is not new, but a combination of rising house prices and rents, tight new housing benefit caps that do not increase in line with the rising rents, and benefit reform, has made central London increasingly inaccessible to people on low incomes in the past three years.

Although the building has been sold, Southwark remains responsible for the evictions at 21 and 22 Park Street, because it sold the houses as vacant. Officials say "police have been notified and we will deal with the issue through the usual legal process". Labour councillor Fiona Colley, Southwark council's cabinet member for regeneration and corporate strategy, said in an emailed statement that there was no doubt the correct decision had been made.

"Occasionally, it makes sense to sell in pockets where land prices are very high. Councils are struggling with huge financial pressures, and Southwark is building more council houses than anyone else, but to fund those we have to think carefully about our priorities. With Park Street, we could have kept homes for two families, or used the proceeds to build 20 new homes for those on our waiting list of 20,000," she said.

But neighbours on Park Street are broadly supportive of the protest. Several of the houses opposite, which date from a similar era, are still owned by the council, and Maureen Lynch, a retired former youth worker, is "terrified" that the £3m price tag may make council staff consider selling the house where she has lived for the past 30 years, and brought up her two children.

"I do understand what they mean about social cleansing. They are selling off the family silver," she said. The pace of development in the area is intense. "Everywhere you go you have cranes, you have ditches, you have dust."

Her son has moved to Stafford because he couldn't afford to live in London. "They couldn't have bought a garage here. The community is being eroded. It has become an area of haves and have-yachts. The only people who can buy here are the loaded gentry or people from other countries who are hoovering up bits of London," she says.